• Abbreviations:
    • MetS : metabolic syndrome
    • WC : waist circumference
    • TG : triglycerides
    • HDL : high-density lipoprotein
    • DBP : diastolic blood pressure
    • Hypertension : Hypertension
    • SBP : systolic blood pressure
    • FBG : Fasting blood glucose
    • BC : bladder cancer

Mendelian Randomization Report [Metabolic Syndrome on bladder cancer]

MetS on BC

Introduction

  • Title: Investigating the causality between MetS on BC

Data Preparation

1- Number of total SNPs in exposure: 9,463,307 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 7,845 SNPs

3- Number of SNPs exposure after clumping : 85 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 73 SNPs

6- Number of SNPs after harmonization (action=2) = 70 SNPs

(rs3949781, rs5112, rs9971210 being palindromic and were removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.76   36.35   45.11   73.95   75.83  421.53

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      7jXcAG     lz4JOx outcome exposure                  MR Egger   70
## 2      7jXcAG     lz4JOx outcome exposure           Weighted median   70
## 3      7jXcAG     lz4JOx outcome exposure Inverse variance weighted   70
## 4      7jXcAG     lz4JOx outcome exposure               Simple mode   70
## 5      7jXcAG     lz4JOx outcome exposure             Weighted mode   70
##               b           se      pval
## 1 -2.717526e-04 0.0006554467 0.6797349
## 2  3.568013e-04 0.0004299056 0.4065655
## 3  2.480041e-04 0.0002884809 0.3899602
## 4  7.860014e-05 0.0009352226 0.9332646
## 5  4.067502e-06 0.0006829852 0.9952654

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      7jXcAG     lz4JOx outcome exposure                  MR Egger 61.42529
## 2      7jXcAG     lz4JOx outcome exposure Inverse variance weighted 62.20519
##   Q_df    Q_pval
## 1   68 0.7003356
## 2   69 0.7058504
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      7jXcAG     lz4JOx outcome exposure    3.841143e-05 4.349532e-05
##        pval
## 1 0.3802849

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd    T-stat
## 1 beta.exposure               Raw    0.0002480041 0.0002739087 0.9054259
## 2 beta.exposure Outlier-corrected              NA           NA        NA
##     P-value
## 1 0.3683906
## 2        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 63.87338
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.717

Radial test

## 
## Radial IVW
## 
##                      Estimate    Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 0.0002480038 0.0002739089 0.9054245 0.3652406
## Iterative        0.0002480038 0.0002739089 0.9054245 0.3652406
## Exact (FE)       0.0002516285 0.0002885022 0.8721890 0.3831053
## Exact (RE)       0.0002512773 0.0002633104 0.9543009 0.3432627
## 
## 
## Residual standard error: 0.949 on 69 degrees of freedom
## 
## F-statistic: 0.82 on 1 and 69 DF, p-value: 0.368
## Q-Statistic for heterogeneity: 62.19634 on 69 DF , p-value: 0.7061283
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##        13        14        39        63 
## 0.3934785 0.3949920 0.1058180 0.4551633
## [1] 13 29 48 63

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      7jXcAG     lz4JOx outcome exposure                  MR Egger   49
## 2      7jXcAG     lz4JOx outcome exposure           Weighted median   49
## 3      7jXcAG     lz4JOx outcome exposure Inverse variance weighted   49
## 4      7jXcAG     lz4JOx outcome exposure               Simple mode   49
## 5      7jXcAG     lz4JOx outcome exposure             Weighted mode   49
##              b           se       pval
## 1 0.0008373382 0.0008464392 0.32760756
## 2 0.0006136787 0.0005149885 0.23340410
## 3 0.0007774423 0.0003614456 0.03148214
## 4 0.0009583264 0.0008833201 0.28337880
## 5 0.0006385041 0.0006720742 0.34684606

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      7jXcAG     lz4JOx outcome exposure                  MR Egger 19.80711
## 2      7jXcAG     lz4JOx outcome exposure Inverse variance weighted 19.81323
##   Q_df    Q_pval
## 1   47 0.9998349
## 2   48 0.9998953
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      7jXcAG     lz4JOx outcome exposure   -4.203219e-06 5.371135e-05
##        pval
## 1 0.9379569

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      7jXcAG     lz4JOx outcome exposure                  MR Egger   49
## 2      7jXcAG     lz4JOx outcome exposure           Weighted median   49
## 3      7jXcAG     lz4JOx outcome exposure Inverse variance weighted   49
## 4      7jXcAG     lz4JOx outcome exposure               Simple mode   49
## 5      7jXcAG     lz4JOx outcome exposure             Weighted mode   49
##              b           se       pval         lo_ci       up_ci       or
## 1 0.0008373382 0.0008464392 0.32760756 -0.0008216827 0.002496359 1.000838
## 2 0.0006136787 0.0005149885 0.23340410 -0.0003956987 0.001623056 1.000614
## 3 0.0007774423 0.0003614456 0.03148214  0.0000690089 0.001485876 1.000778
## 4 0.0009583264 0.0008833201 0.28337880 -0.0007729809 0.002689634 1.000959
## 5 0.0006385041 0.0006720742 0.34684606 -0.0006787612 0.001955769 1.000639
##    or_lci95 or_uci95
## 1 0.9991787 1.002499
## 2 0.9996044 1.001624
## 3 1.0000690 1.001487
## 4 0.9992273 1.002693
## 5 0.9993215 1.001958

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 49 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.001     0.000 0.000, 0.001   0.031
## ------------------------------------------------------------------
## Residual standard error =  0.642 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 19.8132 on 48 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%. 
## F statistic = 67.5.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.001     0.001   0.000 0.002   0.109
##            Weighted median    0.001     0.001   0.000 0.002   0.230
##  Penalized weighted median    0.001     0.001   0.000 0.002   0.230
##                                                                    
##                        IVW    0.001     0.000   0.000 0.001   0.031
##              Penalized IVW    0.001     0.000   0.000 0.001   0.031
##                 Robust IVW    0.001     0.000   0.000 0.001   0.004
##       Penalized robust IVW    0.001     0.000   0.000 0.001   0.004
##                                                                    
##                   MR-Egger    0.001     0.001  -0.001 0.002   0.323
##                (intercept)    0.000     0.000   0.000 0.000   0.938
##         Penalized MR-Egger    0.001     0.001  -0.001 0.002   0.323
##                (intercept)    0.000     0.000   0.000 0.000   0.938
##            Robust MR-Egger    0.001     0.000   0.000 0.002   0.077
##                (intercept)    0.000     0.000   0.000 0.000   0.901
##  Penalized robust MR-Egger    0.001     0.000   0.000 0.002   0.077
##                (intercept)    0.000     0.000   0.000 0.000   0.901

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
7jXcAG lz4JOx exposure outcome 0.0178383 6.54e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] 0.0007821548
## 
## $beta.se
## [1] 0.0003688363
## 
## $beta.p.value
## [1] 0.03395538
## 
## $naive.se
## [1] 0.0003660649
## 
## $chi.sq.test
## [1] 19.78523
##   over.dispersion loss.function     beta.hat      beta.se
## 1           FALSE            l2 0.0007821548 0.0003688363
## 2           FALSE         huber 0.0007821534 0.0003784179
## 3           FALSE         tukey 0.0007765945 0.0003784110
## 4            TRUE            l2 0.0007950524 0.0004204950
## 5            TRUE         huber 0.0007824554 0.0003784268
## 6            TRUE         tukey 0.0007798699 0.0003784242
## 
## MR-Lasso method 
## 
## Number of variants : 49 
## Number of valid instruments : 49 
## Tuning parameter : 0.1785468 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.001     0.000 0.000, 0.001   0.031
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  49 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.001 0.000  0.031 [0.000,0.001]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 49 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.001     0.000 0.000, 0.002   0.032   465.263
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 49 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.001     0.001 -0.001, 0.002   0.349
## ------------------------------------------------------------------

WC on BC

Introduction

  • Title: Investigating the causality between WC on BC

Data Preparation

1- Number of total SNPs in exposure: 9,463,307 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 40,966 SNPs

3- Number of SNPs exposure after clumping : 375 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 338 SNPs

6- Number of SNPs after harmonization (action=2) = 325 SNPs

(rs10406327, rs10887578, rs11666480, rs11778934, rs1405261, rs1441098, rs1454687, rs165656, rs2373980, rs347551, rs3949781, rs4856717, rs654060 being palindromic and were removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.70   34.92   42.79   57.70   59.44  940.08

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      gQWuOt     hk2Grt outcome exposure                  MR Egger  325
## 2      gQWuOt     hk2Grt outcome exposure           Weighted median  325
## 3      gQWuOt     hk2Grt outcome exposure Inverse variance weighted  325
## 4      gQWuOt     hk2Grt outcome exposure               Simple mode  325
## 5      gQWuOt     hk2Grt outcome exposure             Weighted mode  325
##              b           se       pval
## 1 0.0004851254 0.0015935854 0.76100102
## 2 0.0019680361 0.0009068006 0.02998355
## 3 0.0007836522 0.0005521999 0.15585649
## 4 0.0038565942 0.0027013483 0.15435420
## 5 0.0027540038 0.0020488110 0.17982540

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      gQWuOt     hk2Grt outcome exposure                  MR Egger 310.8984
## 2      gQWuOt     hk2Grt outcome exposure Inverse variance weighted 310.9383
##   Q_df   Q_pval
## 1  323 0.675767
## 2  324 0.689309
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      gQWuOt     hk2Grt outcome exposure    4.911427e-06 2.459367e-05
##        pval
## 1 0.8418386

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw    0.0007836522 0.0005409547 1.448647
## 2 beta.exposure Outlier-corrected              NA           NA       NA
##     P-value
## 1 0.1484034
## 2        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 312.9557
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.673

Radial test

## 
## Radial IVW
## 
##                      Estimate    Std.Error  t value  Pr(>|t|)
## Effect (Mod.2nd) 0.0007836521 0.0005409547 1.448646 0.1474363
## Iterative        0.0007836521 0.0005409547 1.448646 0.1474363
## Exact (FE)       0.0007969929 0.0005522305 1.443225 0.1489571
## Exact (RE)       0.0007971043 0.0005467433 1.457913 0.1458331
## 
## 
## Residual standard error: 0.98 on 324 degrees of freedom
## 
## F-statistic: 2.1 on 1 and 324 DF, p-value: 0.148
## Q-Statistic for heterogeneity: 310.9049 on 324 DF , p-value: 0.689785
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##         44         69         87         97        157        161        184 
## 0.02126731 0.22101306 0.01745966 0.31847637 0.01750254 0.02205178 0.22280641 
##        193        202        209        215        216        232        274 
## 0.09906164 0.02447554 0.03537849 0.02763198 0.03682358 0.01686872 0.02093784 
##        285        312 
## 0.02300973 0.02724397
##  [1]  42  69  72  77  97 102 161 165 184 193 202 211 216 223 232 236 292 312

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      gQWuOt     hk2Grt outcome exposure                  MR Egger  300
## 2      gQWuOt     hk2Grt outcome exposure           Weighted median  300
## 3      gQWuOt     hk2Grt outcome exposure Inverse variance weighted  300
## 4      gQWuOt     hk2Grt outcome exposure               Simple mode  300
## 5      gQWuOt     hk2Grt outcome exposure             Weighted mode  300
##             b           se       pval
## 1 0.001438162 0.0023135435 0.53466208
## 2 0.002016313 0.0008781334 0.02166818
## 3 0.001584878 0.0006181852 0.01035455
## 4 0.003779784 0.0028239192 0.18175405
## 5 0.003004811 0.0025216609 0.23436307

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      gQWuOt     hk2Grt outcome exposure                  MR Egger 217.4532
## 2      gQWuOt     hk2Grt outcome exposure Inverse variance weighted 217.4576
##   Q_df    Q_pval
## 1  298 0.9998564
## 2  299 0.9998785
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      gQWuOt     hk2Grt outcome exposure    2.176654e-06 3.307549e-05
##        pval
## 1 0.9475743

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      gQWuOt     hk2Grt outcome exposure                  MR Egger  300
## 2      gQWuOt     hk2Grt outcome exposure           Weighted median  300
## 3      gQWuOt     hk2Grt outcome exposure Inverse variance weighted  300
## 4      gQWuOt     hk2Grt outcome exposure               Simple mode  300
## 5      gQWuOt     hk2Grt outcome exposure             Weighted mode  300
##             b           se       pval         lo_ci       up_ci       or
## 1 0.001438162 0.0023135435 0.53466208 -0.0030963829 0.005972707 1.001439
## 2 0.002016313 0.0008781334 0.02166818  0.0002951711 0.003737454 1.002018
## 3 0.001584878 0.0006181852 0.01035455  0.0003732347 0.002796521 1.001586
## 4 0.003779784 0.0028239192 0.18175405 -0.0017550976 0.009314666 1.003787
## 5 0.003004811 0.0025216609 0.23436307 -0.0019376441 0.007947267 1.003009
##    or_lci95 or_uci95
## 1 0.9969084 1.005991
## 2 1.0002952 1.003744
## 3 1.0003733 1.002800
## 4 0.9982464 1.009358
## 5 0.9980642 1.007979

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 300 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.002     0.001 0.000, 0.003   0.010
## ------------------------------------------------------------------
## Residual standard error =  0.853 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 217.4576 on 299 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%. 
## F statistic = 49.9.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.002     0.001   0.001 0.004   0.005
##            Weighted median    0.002     0.001   0.000 0.004   0.021
##  Penalized weighted median    0.002     0.001   0.000 0.004   0.019
##                                                                    
##                        IVW    0.002     0.001   0.000 0.003   0.010
##              Penalized IVW    0.002     0.001   0.000 0.003   0.010
##                 Robust IVW    0.002     0.001   0.000 0.003   0.008
##       Penalized robust IVW    0.002     0.001   0.000 0.003   0.008
##                                                                    
##                   MR-Egger    0.001     0.002  -0.003 0.006   0.534
##                (intercept)    0.000     0.000   0.000 0.000   0.948
##         Penalized MR-Egger    0.001     0.002  -0.003 0.006   0.534
##                (intercept)    0.000     0.000   0.000 0.000   0.948
##            Robust MR-Egger    0.001     0.002  -0.003 0.005   0.623
##                (intercept)    0.000     0.000   0.000 0.000   0.775
##  Penalized robust MR-Egger    0.001     0.002  -0.003 0.005   0.623
##                (intercept)    0.000     0.000   0.000 0.000   0.775

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
gQWuOt hk2Grt exposure outcome 0.0323754 0.0006007 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] 0.001608248
## 
## $beta.se
## [1] 0.0006327895
## 
## $beta.p.value
## [1] 0.01103711
## 
## $naive.se
## [1] 0.0006263816
## 
## $chi.sq.test
## [1] 217.3606
##   over.dispersion loss.function    beta.hat      beta.se
## 1           FALSE            l2 0.001608248 0.0006327895
## 2           FALSE         huber 0.001623035 0.0006492334
## 3           FALSE         tukey 0.001659829 0.0006492483
## 4            TRUE            l2 0.001621952 0.0007175196
## 5            TRUE         huber 0.001623411 0.0006492399
## 6            TRUE         tukey 0.001660072 0.0006492553
## 
## MR-Lasso method 
## 
## Number of variants : 300 
## Number of valid instruments : 300 
## Tuning parameter : 0.1435915 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.002     0.001 0.000, 0.003   0.010
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  300 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.002 0.001  0.010 [0.000,0.003]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 300 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.002     0.001 0.000, 0.003   0.010   846.644
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 300 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.003     0.002 -0.001, 0.007   0.182
## ------------------------------------------------------------------

TG on BC

Introduction

Data Preparation

1- Number of total SNPs in exposure: 2,439,432 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 3,242 SNPs

3- Number of SNPs exposure after clumping : 55 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 49 SNPs

6- Number of SNPs after harmonization (action=2) = 49 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.86   39.75   54.34  161.67  139.80 1140.06

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      tMn5wl     7jXcAG outcome exposure                  MR Egger   49
## 2      tMn5wl     7jXcAG outcome exposure           Weighted median   49
## 3      tMn5wl     7jXcAG outcome exposure Inverse variance weighted   49
## 4      tMn5wl     7jXcAG outcome exposure               Simple mode   49
## 5      tMn5wl     7jXcAG outcome exposure             Weighted mode   49
##               b           se      pval
## 1 -0.0016251822 0.0007995444 0.0477606
## 2 -0.0010058346 0.0006603498 0.1277126
## 3 -0.0004007591 0.0004863338 0.4099162
## 4 -0.0007659475 0.0011520755 0.5093337
## 5 -0.0010199074 0.0006581437 0.1277890

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      tMn5wl     7jXcAG outcome exposure                  MR Egger 51.56956
## 2      tMn5wl     7jXcAG outcome exposure Inverse variance weighted 55.53372
##   Q_df    Q_pval
## 1   47 0.2997419
## 2   48 0.2120682
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      tMn5wl     7jXcAG outcome exposure    7.299405e-05 3.840251e-05
##         pval
## 1 0.06347554

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd     T-stat
## 1 beta.exposure               Raw   -0.0004007591 0.0004863338 -0.8240411
## 2 beta.exposure Outlier-corrected              NA           NA         NA
##     P-value
## 1 0.4139921
## 2        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 57.3746
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.221

Radial test

## 
## Radial IVW
## 
##                       Estimate    Std.Error    t value  Pr(>|t|)
## Effect (Mod.2nd) -0.0004007595 0.0004863343 -0.8240412 0.4099162
## Iterative        -0.0004007595 0.0004863343 -0.8240412 0.4099162
## Exact (FE)       -0.0004078146 0.0004521674 -0.9019107 0.3671043
## Exact (RE)       -0.0004034230 0.0004359303 -0.9254299 0.3593719
## 
## 
## Residual standard error: 1.076 on 48 degrees of freedom
## 
## F-statistic: 0.68 on 1 and 48 DF, p-value: 0.414
## Q-Statistic for heterogeneity: 55.52826 on 48 DF , p-value: 0.2122145
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##         6        10 
## 0.1119431 0.6940430
## [1] 11 26 33

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      tMn5wl     7jXcAG outcome exposure                  MR Egger   31
## 2      tMn5wl     7jXcAG outcome exposure           Weighted median   31
## 3      tMn5wl     7jXcAG outcome exposure Inverse variance weighted   31
## 4      tMn5wl     7jXcAG outcome exposure               Simple mode   31
## 5      tMn5wl     7jXcAG outcome exposure             Weighted mode   31
##               b           se       pval
## 1 -0.0009272501 0.0012178857 0.45258902
## 2 -0.0010867780 0.0008836880 0.21876414
## 3 -0.0013029307 0.0006466567 0.04391803
## 4 -0.0009568986 0.0014385320 0.51101024
## 5 -0.0009967204 0.0008965354 0.27507739

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      tMn5wl     7jXcAG outcome exposure                  MR Egger 10.70223
## 2      tMn5wl     7jXcAG outcome exposure Inverse variance weighted 10.83474
##   Q_df    Q_pval
## 1   29 0.9992216
## 2   30 0.9994857
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      tMn5wl     7jXcAG outcome exposure   -1.893036e-05 5.200337e-05
##        pval
## 1 0.7184824

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      tMn5wl     7jXcAG outcome exposure                  MR Egger   31
## 2      tMn5wl     7jXcAG outcome exposure           Weighted median   31
## 3      tMn5wl     7jXcAG outcome exposure Inverse variance weighted   31
## 4      tMn5wl     7jXcAG outcome exposure               Simple mode   31
## 5      tMn5wl     7jXcAG outcome exposure             Weighted mode   31
##               b           se       pval        lo_ci         up_ci        or
## 1 -0.0009272501 0.0012178857 0.45258902 -0.003314306  1.459806e-03 0.9990732
## 2 -0.0010867780 0.0008836880 0.21876414 -0.002818806  6.452504e-04 0.9989138
## 3 -0.0013029307 0.0006466567 0.04391803 -0.002570378 -3.548352e-05 0.9986979
## 4 -0.0009568986 0.0014385320 0.51101024 -0.003776421  1.862624e-03 0.9990436
## 5 -0.0009967204 0.0008965354 0.27507739 -0.002753930  7.604889e-04 0.9990038
##    or_lci95  or_uci95
## 1 0.9966912 1.0014609
## 2 0.9971852 1.0006455
## 3 0.9974329 0.9999645
## 4 0.9962307 1.0018644
## 5 0.9972499 1.0007608

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 31 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW   -0.001     0.001 -0.003, 0.000   0.044
## ------------------------------------------------------------------
## Residual standard error =  0.601 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 10.8347 on 30 degrees of freedom, (p-value = 0.9995). I^2 = 0.0%. 
## F statistic = 124.1.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median   -0.001     0.001  -0.003 0.001   0.162
##            Weighted median   -0.001     0.001  -0.003 0.001   0.243
##  Penalized weighted median   -0.001     0.001  -0.003 0.001   0.243
##                                                                    
##                        IVW   -0.001     0.001  -0.003 0.000   0.044
##              Penalized IVW   -0.001     0.001  -0.003 0.000   0.044
##                 Robust IVW   -0.001     0.000  -0.002 0.000   0.022
##       Penalized robust IVW   -0.001     0.000  -0.002 0.000   0.022
##                                                                    
##                   MR-Egger   -0.001     0.001  -0.003 0.001   0.446
##                (intercept)    0.000     0.000   0.000 0.000   0.716
##         Penalized MR-Egger   -0.001     0.001  -0.003 0.001   0.446
##                (intercept)    0.000     0.000   0.000 0.000   0.716
##            Robust MR-Egger   -0.001     0.001  -0.003 0.000   0.172
##                (intercept)    0.000     0.000   0.000 0.000   0.930
##  Penalized robust MR-Egger   -0.001     0.001  -0.003 0.000   0.172
##                (intercept)    0.000     0.000   0.000 0.000   0.930

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
tMn5wl 7jXcAG exposure outcome 0.0180328 4e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] -0.001306734
## 
## $beta.se
## [1] 0.0006543805
## 
## $beta.p.value
## [1] 0.04583574
## 
## $naive.se
## [1] 0.0006515952
## 
## $chi.sq.test
## [1] 10.82295
##   over.dispersion loss.function     beta.hat      beta.se
## 1           FALSE            l2 -0.001306734 0.0006543805
## 2           FALSE         huber -0.001306734 0.0006713799
## 3           FALSE         tukey -0.001264176 0.0006713349
## 4            TRUE            l2 -0.001337558 0.0007611713
## 5            TRUE         huber -0.001304389 0.0006713843
## 6            TRUE         tukey -0.001271652 0.0006713497
## 
## MR-Lasso method 
## 
## Number of variants : 31 
## Number of valid instruments : 31 
## Tuning parameter : 0.2424016 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure   -0.001     0.001 -0.003, 0.000   0.044
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  31 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC   -0.001 0.001  0.044 [-0.003,0.000]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 31 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW   -0.001     0.001 -0.003, 0.000   0.044   685.513
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 31 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE   -0.001     0.001 -0.003, 0.001   0.317
## ------------------------------------------------------------------

HDL on BC

Introduction

Data Preparation

1- Number of total SNPs in exposure: 120,671 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 1,628 SNPs

3- Number of SNPs exposure after clumping : 42 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 40 SNPs

6- Number of SNPs after harmonization (action=2) = 40 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   34.42   42.06   57.36  135.73  120.65 1817.10

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      JI02GY     hk2Grt outcome exposure                  MR Egger   40
## 2      JI02GY     hk2Grt outcome exposure           Weighted median   40
## 3      JI02GY     hk2Grt outcome exposure Inverse variance weighted   40
## 4      JI02GY     hk2Grt outcome exposure               Simple mode   40
## 5      JI02GY     hk2Grt outcome exposure             Weighted mode   40
##               b           se      pval
## 1 -0.0003130527 0.0008773012 0.7231886
## 2 -0.0005919845 0.0005767193 0.3046706
## 3  0.0002086744 0.0004843317 0.6665774
## 4  0.0007916117 0.0012495937 0.5301081
## 5 -0.0007112743 0.0005322064 0.1891432

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      JI02GY     hk2Grt outcome exposure                  MR Egger 60.39705
## 2      JI02GY     hk2Grt outcome exposure Inverse variance weighted 61.21010
##   Q_df     Q_pval
## 1   38 0.01185218
## 2   39 0.01305900
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      JI02GY     hk2Grt outcome exposure    4.214987e-05 5.893206e-05
##        pval
## 1 0.4788397

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd    T-stat
## 1 beta.exposure               Raw    2.086744e-04 0.0004843317 0.4308501
## 2 beta.exposure Outlier-corrected    9.034355e-05 0.0004430422 0.2039163
##     P-value
## 1 0.6689494
## 2 0.8395070
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 67.98238
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.013
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  3.673356e-09      1
## 2  2.808632e-08      1
## 3  7.851406e-10      1
## 4  1.223175e-07    0.4
## 5  2.731639e-09      1
## 6  1.217620e-07      1
## 7  5.484050e-09      1
## 8  5.327204e-08      1
## 9  1.397143e-07   0.48
## 10 1.361036e-08      1
## 11 2.095919e-08      1
## 12 3.562765e-10      1
## 13 2.118310e-08      1
## 14 1.230648e-08      1
## 15 4.935965e-08      1
## 16 3.174821e-09      1
## 17 1.956409e-09      1
## 18 8.526203e-08      1
## 19 1.704063e-08      1
## 20 1.444154e-08      1
## 21 6.701960e-12      1
## 22 7.941793e-09      1
## 23 4.373821e-08      1
## 24 8.307344e-08      1
## 25 1.418331e-07    0.8
## 26 7.822265e-08      1
## 27 8.872155e-09      1
## 28 1.308734e-10      1
## 29 1.137428e-10      1
## 30 2.796098e-08      1
## 31 3.056937e-08      1
## 32 3.743604e-13      1
## 33 7.461141e-09      1
## 34 2.076311e-07   0.12
## 35 1.712467e-08      1
## 36 4.623446e-08      1
## 37 1.024587e-08      1
## 38 4.652940e-08      1
## 39 5.177744e-07  <0.04
## 40 1.224732e-11      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 39
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      130.9787 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.384

Radial test

## 
## Radial IVW
## 
##                      Estimate    Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 0.0002086733 0.0004843315 0.4308481 0.6665788
## Iterative        0.0002086733 0.0004843315 0.4308481 0.6665788
## Exact (FE)       0.0002091666 0.0003866121 0.5410246 0.5884906
## Exact (RE)       0.0002103403 0.0006001667 0.3504697 0.7278722
## 
## 
## Residual standard error: 1.253 on 39 degrees of freedom
## 
## F-statistic: 0.19 on 1 and 39 DF, p-value: 0.669
## Q-Statistic for heterogeneity: 61.20676 on 39 DF , p-value: 0.01306847
## 
##  Outliers detected 
## Number of iterations = 2
##         SNP Q_statistic      p.value
## 1 rs8044791    11.60761 0.0006568235

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##       34 
## 1.373054
## [1] 34 39

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      JI02GY     hk2Grt outcome exposure                  MR Egger   28
## 2      JI02GY     hk2Grt outcome exposure           Weighted median   28
## 3      JI02GY     hk2Grt outcome exposure Inverse variance weighted   28
## 4      JI02GY     hk2Grt outcome exposure               Simple mode   28
## 5      JI02GY     hk2Grt outcome exposure             Weighted mode   28
##             b           se       pval
## 1 0.001444222 0.0016993868 0.40316735
## 2 0.001223993 0.0008339964 0.14220650
## 3 0.001495770 0.0006210339 0.01601752
## 4 0.001005600 0.0015260057 0.51549289
## 5 0.001005600 0.0014169252 0.48397127

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      JI02GY     hk2Grt outcome exposure                  MR Egger 8.744656
## 2      JI02GY     hk2Grt outcome exposure Inverse variance weighted 8.745718
##   Q_df    Q_pval
## 1   26 0.9993785
## 2   27 0.9996541
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      JI02GY     hk2Grt outcome exposure    2.796185e-06 8.580547e-05
##        pval
## 1 0.9742524

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      JI02GY     hk2Grt outcome exposure                  MR Egger   28
## 2      JI02GY     hk2Grt outcome exposure           Weighted median   28
## 3      JI02GY     hk2Grt outcome exposure Inverse variance weighted   28
## 4      JI02GY     hk2Grt outcome exposure               Simple mode   28
## 5      JI02GY     hk2Grt outcome exposure             Weighted mode   28
##             b           se       pval         lo_ci       up_ci       or
## 1 0.001444222 0.0016993868 0.40316735 -0.0018865764 0.004775020 1.001445
## 2 0.001223993 0.0008339964 0.14220650 -0.0004106401 0.002858626 1.001225
## 3 0.001495770 0.0006210339 0.01601752  0.0002785437 0.002712996 1.001497
## 4 0.001005600 0.0015260057 0.51549289 -0.0019853714 0.003996571 1.001006
## 5 0.001005600 0.0014169252 0.48397127 -0.0017715737 0.003782773 1.001006
##    or_lci95 or_uci95
## 1 0.9981152 1.004786
## 2 0.9995894 1.002863
## 3 1.0002786 1.002717
## 4 0.9980166 1.004005
## 5 0.9982300 1.003790

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 28 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.001     0.001 0.000, 0.003   0.016
## ------------------------------------------------------------------
## Residual standard error =  0.569 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 8.7457 on 27 degrees of freedom, (p-value = 0.9997). I^2 = 0.0%. 
## F statistic = 73.8.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.001     0.001   0.000 0.003   0.116
##            Weighted median    0.001     0.001   0.000 0.003   0.135
##  Penalized weighted median    0.001     0.001   0.000 0.003   0.135
##                                                                    
##                        IVW    0.001     0.001   0.000 0.003   0.016
##              Penalized IVW    0.001     0.001   0.000 0.003   0.016
##                 Robust IVW    0.001     0.001   0.000 0.002   0.004
##       Penalized robust IVW    0.001     0.001   0.000 0.002   0.004
##                                                                    
##                   MR-Egger    0.001     0.002  -0.002 0.005   0.395
##                (intercept)    0.000     0.000   0.000 0.000   0.974
##         Penalized MR-Egger    0.001     0.002  -0.002 0.005   0.395
##                (intercept)    0.000     0.000   0.000 0.000   0.974
##            Robust MR-Egger    0.001     0.001  -0.001 0.004   0.286
##                (intercept)    0.000     0.000   0.000 0.000   0.993
##  Penalized robust MR-Egger    0.001     0.001  -0.001 0.004   0.286
##                (intercept)    0.000     0.000   0.000 0.000   0.993

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
JI02GY hk2Grt exposure outcome 0.0096945 3.9e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] 0.001502448
## 
## $beta.se
## [1] 0.0006337508
## 
## $beta.p.value
## [1] 0.01775326
## 
## $naive.se
## [1] 0.0006293192
## 
## $chi.sq.test
## [1] 8.72018
##   over.dispersion loss.function    beta.hat      beta.se
## 1           FALSE            l2 0.001502448 0.0006337508
## 2           FALSE         huber 0.001502448 0.0006502142
## 3           FALSE         tukey 0.001490996 0.0006501873
## 4            TRUE            l2 0.001505703 0.0007133709
## 5            TRUE         huber 0.001504387 0.0006502470
## 6            TRUE         tukey 0.001492426 0.0006502194
## 
## MR-Lasso method 
## 
## Number of variants : 28 
## Number of valid instruments : 28 
## Tuning parameter : 0.1920885 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.001     0.001 0.000, 0.003   0.016
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  28 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.002 0.001  0.016 [0.000,0.003]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 28 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.002     0.001 0.000, 0.003   0.016   385.443
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 28 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.001     0.002 -0.002, 0.004   0.521
## ------------------------------------------------------------------

DBP on BC

Introduction

  • Title: Investigating the causality between DBP on BC

Data Preparation

1- Number of total SNPs in exposure: 7,160,619 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 83,547 SNPs

3- Number of SNPs exposure after clumping : 455 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 455 SNPs

6- Number of SNPs after harmonization (action=2) = 446 SNPs

(rs11664194, rs12321, rs1528293, rs3802517, rs61912333, rs710249, rs7694000, rs9893005, rs990619 being palindromic and were removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.65   38.96   51.43   79.45   82.04  815.82

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      hk2Grt     hk2Grt outcome exposure                  MR Egger  446
## 2      hk2Grt     hk2Grt outcome exposure           Weighted median  446
## 3      hk2Grt     hk2Grt outcome exposure Inverse variance weighted  446
## 4      hk2Grt     hk2Grt outcome exposure               Simple mode  446
## 5      hk2Grt     hk2Grt outcome exposure             Weighted mode  446
##               b           se       pval
## 1  1.584565e-04 1.108474e-04 0.15356334
## 2  9.376863e-05 6.812295e-05 0.16867871
## 3  9.844204e-05 4.549784e-05 0.03049015
## 4 -1.233739e-05 2.139253e-04 0.95403618
## 5  6.068265e-05 1.569924e-04 0.69928713

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      hk2Grt     hk2Grt outcome exposure                  MR Egger 542.9292
## 2      hk2Grt     hk2Grt outcome exposure Inverse variance weighted 543.3604
##   Q_df       Q_pval
## 1  444 0.0008949034
## 2  445 0.0009569186
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      hk2Grt     hk2Grt outcome exposure   -1.202335e-05 2.024738e-05
##        pval
## 1 0.5529333

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw    9.844204e-05 4.549784e-05 2.163664
## 2 beta.exposure Outlier-corrected    1.051567e-04 4.504968e-05 2.334239
##      P-value
## 1 0.03102167
## 2 0.02002836
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 545.9811
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.001
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs Pvalue
## 1   3.494752e-08      1
## 2   1.122266e-10      1
## 3   6.238668e-10      1
## 4   1.051785e-08      1
## 5   1.470111e-07      1
## 6   4.335494e-08      1
## 7   2.030694e-07      1
## 8   9.434263e-14      1
## 9   7.271934e-09      1
## 10  7.158172e-15      1
## 11  1.589175e-07      1
## 12  4.280856e-08      1
## 13  5.319715e-08      1
## 14  8.272285e-08      1
## 15  9.354273e-08      1
## 16  7.396646e-08      1
## 17  7.542125e-08      1
## 18  1.908858e-08      1
## 19  9.888472e-08      1
## 20  1.372085e-09      1
## 21  7.105824e-10      1
## 22  5.359425e-09      1
## 23  2.436083e-08      1
## 24  3.898601e-07      1
## 25  1.598062e-07      1
## 26  3.726933e-08      1
## 27  1.746510e-08      1
## 28  6.069109e-10      1
## 29  2.151516e-09      1
## 30  2.596776e-07      1
## 31  3.740862e-08      1
## 32  3.175039e-12      1
## 33  5.592793e-09      1
## 34  3.452744e-08      1
## 35  4.026893e-09      1
## 36  6.598515e-08      1
## 37  6.543357e-09      1
## 38  2.194404e-09      1
## 39  2.602232e-08      1
## 40  4.327267e-08      1
## 41  5.646942e-09      1
## 42  7.955735e-10      1
## 43  1.501272e-08      1
## 44  3.253714e-08      1
## 45  8.857369e-09      1
## 46  4.425659e-08      1
## 47  7.259049e-09      1
## 48  6.423836e-09      1
## 49  1.251701e-09      1
## 50  1.944914e-08      1
## 51  3.368495e-10      1
## 52  1.540923e-12      1
## 53  2.965514e-12      1
## 54  6.477533e-09      1
## 55  8.778367e-09      1
## 56  1.175469e-07      1
## 57  7.334799e-08      1
## 58  2.394569e-08      1
## 59  3.907328e-09      1
## 60  1.054809e-10      1
## 61  3.369967e-08      1
## 62  4.267579e-08      1
## 63  8.935864e-08      1
## 64  4.617676e-08      1
## 65  3.533685e-13      1
## 66  3.097187e-11      1
## 67  7.067225e-09      1
## 68  7.290375e-08      1
## 69  5.990737e-08      1
## 70  9.979258e-09      1
## 71  3.657902e-10      1
## 72  6.837408e-08      1
## 73  2.562786e-08      1
## 74  3.410963e-08      1
## 75  1.449744e-11      1
## 76  2.019221e-08      1
## 77  1.795945e-08      1
## 78  2.258350e-08      1
## 79  2.610347e-08      1
## 80  2.290217e-08      1
## 81  1.188651e-07      1
## 82  1.133472e-07      1
## 83  1.457607e-08      1
## 84  1.243555e-08      1
## 85  1.529449e-08      1
## 86  3.296488e-08      1
## 87  1.068351e-08      1
## 88  7.706082e-08      1
## 89  1.858568e-08      1
## 90  5.191788e-09      1
## 91  7.700558e-11      1
## 92  1.849807e-07      1
## 93  1.287488e-08      1
## 94  1.809531e-09      1
## 95  5.520811e-08      1
## 96  4.831115e-09      1
## 97  9.358228e-08      1
## 98  4.738097e-09      1
## 99  7.831913e-09      1
## 100 1.229642e-08      1
## 101 1.216162e-08      1
## 102 2.761362e-09      1
## 103 3.408916e-08      1
## 104 2.398281e-07 <0.446
## 105 1.562692e-07      1
## 106 2.910165e-09      1
## 107 8.901358e-08      1
## 108 4.501040e-08      1
## 109 2.477586e-09      1
## 110 1.364799e-08      1
## 111 3.375990e-08      1
## 112 5.788909e-11      1
## 113 2.814217e-09      1
## 114 9.205500e-10      1
## 115 4.615619e-08      1
## 116 1.762824e-08      1
## 117 2.101477e-07      1
## 118 2.855074e-08      1
## 119 6.041618e-11      1
## 120 1.407384e-10      1
## 121 3.079210e-08      1
## 122 4.938622e-10      1
## 123 8.391678e-09      1
## 124 1.562852e-07      1
## 125 2.669239e-08      1
## 126 6.315286e-09      1
## 127 3.666752e-08      1
## 128 1.261461e-09      1
## 129 2.166685e-07      1
## 130 1.068885e-08      1
## 131 1.100314e-09      1
## 132 1.215884e-07      1
## 133 1.548849e-08      1
## 134 4.761853e-08      1
## 135 1.619127e-09      1
## 136 9.895721e-09      1
## 137 1.531604e-08      1
## 138 1.405182e-08      1
## 139 7.749070e-09      1
## 140 4.131452e-08      1
## 141 2.386472e-08      1
## 142 1.232109e-08      1
## 143 2.000070e-08      1
## 144 5.275279e-09      1
## 145 2.352506e-08      1
## 146 1.143125e-07      1
## 147 4.033292e-07      1
## 148 4.017055e-11      1
## 149 3.672126e-07      1
## 150 4.488738e-08      1
## 151 4.970710e-11      1
## 152 3.712056e-08      1
## 153 2.548270e-09      1
## 154 5.759132e-08      1
## 155 1.343310e-08      1
## 156 3.047963e-09      1
## 157 3.229626e-08      1
## 158 1.891500e-08      1
## 159 3.639551e-10      1
## 160 1.189555e-08      1
## 161 3.655699e-09      1
## 162 3.002712e-09      1
## 163 4.424768e-08      1
## 164 4.910408e-11      1
## 165 3.630377e-09      1
## 166 1.390415e-09      1
## 167 3.872951e-08      1
## 168 2.015923e-09      1
## 169 4.352049e-08      1
## 170 7.943856e-12      1
## 171 7.174395e-10      1
## 172 1.088992e-09      1
## 173 7.810261e-09      1
## 174 2.221059e-07      1
## 175 2.675946e-09      1
## 176 3.398323e-10      1
## 177 3.767577e-08      1
## 178 1.332644e-09      1
## 179 1.315240e-09      1
## 180 1.794777e-09      1
## 181 1.376269e-08      1
## 182 2.846275e-08      1
## 183 2.341780e-08      1
## 184 5.478941e-08      1
## 185 2.206742e-10      1
## 186 2.767193e-08      1
## 187 9.544680e-09      1
## 188 6.468985e-08      1
## 189 8.018477e-08      1
## 190 9.472814e-08      1
## 191 2.565796e-08      1
## 192 4.117331e-09      1
## 193 1.894480e-13      1
## 194 5.064719e-08      1
## 195 2.802831e-09      1
## 196 7.909957e-08      1
## 197 1.999979e-09      1
## 198 3.915755e-09      1
## 199 6.523344e-08      1
## 200 1.692635e-08      1
## 201 6.386759e-08      1
## 202 1.912406e-09      1
## 203 7.681085e-14      1
## 204 5.180913e-09      1
## 205 2.943188e-08      1
## 206 9.428593e-09      1
## 207 1.384397e-11      1
## 208 2.061798e-08      1
## 209 2.082810e-09      1
## 210 9.461796e-09      1
## 211 2.741144e-08      1
## 212 4.417919e-10      1
## 213 2.393055e-07      1
## 214 2.820543e-08      1
## 215 1.005754e-08      1
## 216 8.327477e-09      1
## 217 6.791523e-10      1
## 218 4.329200e-08      1
## 219 2.241462e-08      1
## 220 1.215696e-07      1
## 221 9.266263e-09      1
## 222 8.623009e-08      1
## 223 7.542736e-09      1
## 224 1.000647e-08      1
## 225 3.389715e-08      1
## 226 1.090958e-07      1
## 227 3.274040e-09      1
## 228 1.013540e-08      1
## 229 8.376612e-10      1
## 230 8.591931e-09      1
## 231 2.819185e-09      1
## 232 7.891864e-09      1
## 233 1.546864e-08      1
## 234 4.566404e-08      1
## 235 4.149129e-09      1
## 236 3.934712e-08      1
## 237 5.138422e-08      1
## 238 8.684786e-09      1
## 239 2.652878e-08      1
## 240 7.755591e-08      1
## 241 1.140448e-08      1
## 242 4.565129e-08      1
## 243 3.419570e-08      1
## 244 4.571673e-10      1
## 245 1.581720e-07      1
## 246 2.044933e-08      1
## 247 2.622144e-08      1
## 248 2.013031e-09      1
## 249 7.168519e-08      1
## 250 3.931480e-08      1
## 251 5.092270e-09      1
## 252 3.891686e-09      1
## 253 1.720015e-08      1
## 254 8.548687e-09      1
## 255 2.079429e-08      1
## 256 1.624362e-10      1
## 257 4.881034e-09      1
## 258 5.857779e-08      1
## 259 1.653336e-07      1
## 260 5.771988e-09      1
## 261 5.559321e-09      1
## 262 1.499765e-09      1
## 263 1.368887e-09      1
## 264 1.309164e-08      1
## 265 9.410937e-10      1
## 266 3.848171e-08      1
## 267 2.596144e-10      1
## 268 1.508558e-08      1
## 269 9.036458e-08      1
## 270 5.161458e-09      1
## 271 3.342602e-08      1
## 272 1.322961e-08      1
## 273 1.397189e-09      1
## 274 1.002212e-15      1
## 275 3.602754e-08      1
## 276 3.382611e-09      1
## 277 7.191612e-08      1
## 278 1.181086e-08      1
## 279 2.937976e-09      1
## 280 6.473575e-09      1
## 281 4.078905e-09      1
## 282 3.011140e-10      1
## 283 1.677755e-08      1
## 284 2.891495e-08      1
## 285 3.332743e-08      1
## 286 5.387389e-08      1
## 287 4.179548e-09      1
## 288 3.217140e-08      1
## 289 1.881992e-10      1
## 290 3.294855e-08      1
## 291 8.787731e-09      1
## 292 1.284272e-08      1
## 293 1.829593e-08      1
## 294 5.291597e-07  0.892
## 295 1.409531e-09      1
## 296 2.037881e-09      1
## 297 1.538913e-07      1
## 298 3.164006e-08      1
## 299 2.682219e-08      1
## 300 9.585501e-08      1
## 301 5.141773e-09      1
## 302 7.442834e-11      1
## 303 1.221111e-07      1
## 304 5.382967e-08      1
## 305 4.236679e-08      1
## 306 7.772311e-08      1
## 307 2.097772e-07      1
## 308 1.656485e-08      1
## 309 1.196828e-09      1
## 310 1.503588e-08      1
## 311 4.587262e-09      1
## 312 5.119804e-08      1
## 313 6.213046e-08      1
## 314 1.226821e-08      1
## 315 6.440880e-09      1
## 316 2.457595e-07      1
## 317 1.017328e-08      1
## 318 4.902772e-09      1
## 319 1.927357e-08      1
## 320 3.183236e-08      1
## 321 2.863878e-08      1
## 322 3.205512e-08      1
## 323 2.853009e-08      1
## 324 9.326727e-08      1
## 325 5.877908e-08      1
## 326 1.610183e-08      1
## 327 1.000682e-07      1
## 328 1.055403e-08      1
## 329 3.694089e-10      1
## 330 7.689650e-09      1
## 331 2.813979e-08      1
## 332 3.622405e-08      1
## 333 1.743958e-08      1
## 334 1.961867e-08      1
## 335 6.648930e-11      1
## 336 1.388771e-07      1
## 337 5.140729e-08      1
## 338 9.807835e-09      1
## 339 1.067900e-10      1
## 340 5.092898e-10      1
## 341 4.285188e-10      1
## 342 4.819442e-10      1
## 343 3.528895e-08      1
## 344 5.468563e-09      1
## 345 1.736779e-08      1
## 346 1.056558e-08      1
## 347 1.754000e-08      1
## 348 2.754882e-08      1
## 349 1.158190e-07      1
## 350 3.900430e-08      1
## 351 2.384305e-08      1
## 352 4.602547e-09      1
## 353 3.342621e-09      1
## 354 8.782089e-08      1
## 355 1.410340e-09      1
## 356 2.311352e-10      1
## 357 6.000694e-10      1
## 358 7.485900e-08      1
## 359 8.320497e-08      1
## 360 4.699383e-10      1
## 361 2.627152e-08      1
## 362 7.482176e-08      1
## 363 1.338385e-07      1
## 364 4.083805e-10      1
## 365 1.902248e-07      1
## 366 1.407096e-07      1
## 367 1.133808e-07      1
## 368 1.054993e-08      1
## 369 6.609055e-09      1
## 370 3.402952e-10      1
## 371 3.476294e-09      1
## 372 9.677225e-08      1
## 373 6.035548e-08      1
## 374 6.776867e-08      1
## 375 5.516510e-09      1
## 376 3.425471e-09      1
## 377 3.243789e-08      1
## 378 1.969842e-08      1
## 379 8.881662e-08      1
## 380 1.766979e-09      1
## 381 3.719197e-09      1
## 382 8.625666e-09      1
## 383 1.169203e-12      1
## 384 2.295414e-07      1
## 385 6.660043e-09      1
## 386 7.913456e-09      1
## 387 1.253854e-09      1
## 388 8.356785e-07      1
## 389 6.747454e-09      1
## 390 4.961575e-10      1
## 391 5.212303e-08      1
## 392 2.472364e-08      1
## 393 1.325260e-08      1
## 394 1.368668e-09      1
## 395 2.467813e-07      1
## 396 1.414774e-07      1
## 397 2.170069e-08      1
## 398 2.358693e-09      1
## 399 9.653333e-09      1
## 400 5.834260e-08      1
## 401 4.733761e-08      1
## 402 1.313626e-08      1
## 403 6.205723e-11      1
## 404 8.654842e-09      1
## 405 2.736124e-09      1
## 406 1.005882e-07      1
## 407 4.475767e-08      1
## 408 3.981422e-08      1
## 409 6.445705e-09      1
## 410 5.739364e-10      1
## 411 1.650252e-08      1
## 412 5.106255e-08      1
## 413 7.685999e-09      1
## 414 2.892517e-08      1
## 415 2.190754e-08      1
## 416 1.274279e-08      1
## 417 9.765113e-09      1
## 418 3.819656e-13      1
## 419 5.124018e-09      1
## 420 1.159072e-07      1
## 421 9.578797e-12      1
## 422 1.284437e-09      1
## 423 6.694788e-10      1
## 424 1.946331e-07      1
## 425 2.203089e-08      1
## 426 4.267980e-09      1
## 427 1.348986e-08      1
## 428 6.036689e-10      1
## 429 3.132483e-08      1
## 430 5.427043e-09      1
## 431 1.228397e-08      1
## 432 8.544078e-09      1
## 433 1.331752e-08      1
## 434 2.560210e-08      1
## 435 1.950245e-08      1
## 436 2.149330e-11      1
## 437 4.244444e-09      1
## 438 2.119309e-08      1
## 439 9.014149e-09      1
## 440 2.120335e-10      1
## 441 1.113387e-10      1
## 442 7.895029e-09      1
## 443 5.968835e-10      1
## 444 1.088935e-08      1
## 445 7.813987e-08      1
## 446 6.854641e-08      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 104
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##     -6.385405 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.89

Radial test

## 
## Radial IVW
## 
##                      Estimate    Std.Error  t value   Pr(>|t|)
## Effect (Mod.2nd) 9.844203e-05 4.549784e-05 2.163664 0.03049016
## Iterative        9.844204e-05 4.549784e-05 2.163664 0.03049015
## Exact (FE)       9.305751e-05 4.117733e-05 2.259921 0.02382614
## Exact (RE)       9.971526e-05 4.555699e-05 2.188803 0.02913015
## 
## 
## Residual standard error: 1.105 on 445 degrees of freedom
## 
## F-statistic: 4.68 on 1 and 445 DF, p-value: 0.031
## Q-Statistic for heterogeneity: 543.2727 on 445 DF , p-value: 0.0009652871
## 
##  No significant outliers 
## Number of iterations = 1
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##          7         24         30         56        103        117        124 
## 0.01269078 0.07162858 0.02476856 0.03050298 0.02209659 0.08328175 0.05693010 
##        129        147        149        174        214        226        294 
## 0.02332969 0.08542978 0.06992192 0.01648396 0.01123118 0.03464593 0.03373624 
##        307        358        367        374        384        388        395 
## 0.07010790 0.02261226 0.04054549 0.02378892 0.04476658 0.23953629 0.05763937
##  [1]   5   7  11  24  25  30  92 104 105 117 124 129 147 149 174 213 245 259 294
## [20] 297 307 316 365 384 388 395 424

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      hk2Grt     hk2Grt outcome exposure                  MR Egger  407
## 2      hk2Grt     hk2Grt outcome exposure           Weighted median  407
## 3      hk2Grt     hk2Grt outcome exposure Inverse variance weighted  407
## 4      hk2Grt     hk2Grt outcome exposure               Simple mode  407
## 5      hk2Grt     hk2Grt outcome exposure             Weighted mode  407
##              b           se        pval
## 1 1.235639e-04 1.205534e-04 0.305988258
## 2 9.377856e-05 7.055939e-05 0.183823989
## 3 1.186416e-04 4.584136e-05 0.009650931
## 4 1.414102e-05 2.020524e-04 0.944238537
## 5 5.938085e-05 1.397076e-04 0.671035221

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      hk2Grt     hk2Grt outcome exposure                  MR Egger 360.4895
## 2      hk2Grt     hk2Grt outcome exposure Inverse variance weighted 360.4914
##   Q_df    Q_pval
## 1  405 0.9453739
## 2  406 0.9492179
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      hk2Grt     hk2Grt outcome exposure   -9.153322e-07 2.073397e-05
##        pval
## 1 0.9648094

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      hk2Grt     hk2Grt outcome exposure                  MR Egger  407
## 2      hk2Grt     hk2Grt outcome exposure           Weighted median  407
## 3      hk2Grt     hk2Grt outcome exposure Inverse variance weighted  407
## 4      hk2Grt     hk2Grt outcome exposure               Simple mode  407
## 5      hk2Grt     hk2Grt outcome exposure             Weighted mode  407
##              b           se        pval         lo_ci        up_ci       or
## 1 1.235639e-04 1.205534e-04 0.305988258 -1.127208e-04 0.0003598485 1.000124
## 2 9.377856e-05 7.055939e-05 0.183823989 -4.451785e-05 0.0002320750 1.000094
## 3 1.186416e-04 4.584136e-05 0.009650931  2.879257e-05 0.0002084907 1.000119
## 4 1.414102e-05 2.020524e-04 0.944238537 -3.818817e-04 0.0004101638 1.000014
## 5 5.938085e-05 1.397076e-04 0.671035221 -2.144461e-04 0.0003332078 1.000059
##    or_lci95 or_uci95
## 1 0.9998873 1.000360
## 2 0.9999555 1.000232
## 3 1.0000288 1.000209
## 4 0.9996182 1.000410
## 5 0.9997856 1.000333

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 407 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.000     0.000 0.000, 0.000   0.010
## ------------------------------------------------------------------
## Residual standard error =  0.942 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 360.4914 on 406 degrees of freedom, (p-value = 0.9492). I^2 = 0.0%. 
## F statistic = 70.2.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.000     0.000   0.000 0.000   0.312
##            Weighted median    0.000     0.000   0.000 0.000   0.185
##  Penalized weighted median    0.000     0.000   0.000 0.000   0.212
##                                                                    
##                        IVW    0.000     0.000   0.000 0.000   0.010
##              Penalized IVW    0.000     0.000   0.000 0.000   0.012
##                 Robust IVW    0.000     0.000   0.000 0.000   0.018
##       Penalized robust IVW    0.000     0.000   0.000 0.000   0.018
##                                                                    
##                   MR-Egger    0.000     0.000   0.000 0.000   0.305
##                (intercept)    0.000     0.000   0.000 0.000   0.965
##         Penalized MR-Egger    0.000     0.000   0.000 0.000   0.281
##                (intercept)    0.000     0.000   0.000 0.000   0.902
##            Robust MR-Egger    0.000     0.000   0.000 0.000   0.097
##                (intercept)    0.000     0.000   0.000 0.000   0.612
##  Penalized robust MR-Egger    0.000     0.000   0.000 0.000   0.096
##                (intercept)    0.000     0.000   0.000 0.000   0.609

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
hk2Grt hk2Grt exposure outcome 0.0376853 0.0009837 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] 0.0001201561
## 
## $beta.se
## [1] 4.654834e-05
## 
## $beta.p.value
## [1] 0.009842361
## 
## $naive.se
## [1] 4.62152e-05
## 
## $chi.sq.test
## [1] 360.4059
##   over.dispersion loss.function     beta.hat      beta.se
## 1           FALSE            l2 0.0001201561 4.654834e-05
## 2           FALSE         huber 0.0001065602 4.775510e-05
## 3           FALSE         tukey 0.0001048152 4.775490e-05
## 4            TRUE            l2 0.0001187222 5.359789e-05
## 5            TRUE         huber 0.0001070403 4.775532e-05
## 6            TRUE         tukey 0.0001065842 4.775534e-05
## 
## MR-Lasso method 
## 
## Number of variants : 407 
## Number of valid instruments : 407 
## Tuning parameter : 0.1338801 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.000     0.000 0.000, 0.000   0.010
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  407 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.000 0.000  0.009 [0.000,0.000]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 407 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.000     0.000 0.000, 0.000   0.010  1395.739
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 407 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.000     0.000 0.000, 0.000   0.597
## ------------------------------------------------------------------

Hypertension on BC

Introduction

  • Title: Investigating the causality between HBP on BC

    • Exposure: Hypertension, GWAS summary statistics: OpenGWAS | Reference paper: Elsworth B et al., 2018
    • Sample size: 462,933 , Number of cases: 119,731 , Number of controls: 343,202
    • Ancestry: European
    • Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
    • Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
    • Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 9,851,867 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 24,844 SNPs

3- Number of SNPs exposure after clumping : 225 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 205 SNPs

6- Number of SNPs after harmonization (action=2) = 199 SNPs

(rs10786156, rs10995311, rs2046645, rs6926537, rs7171632, rs7310615 being palindromic and were removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.76   35.42   44.79   60.20   62.88  462.71

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      MfEccK     hk2Grt outcome exposure                  MR Egger  199
## 2      MfEccK     hk2Grt outcome exposure           Weighted median  199
## 3      MfEccK     hk2Grt outcome exposure Inverse variance weighted  199
## 4      MfEccK     hk2Grt outcome exposure               Simple mode  199
## 5      MfEccK     hk2Grt outcome exposure             Weighted mode  199
##              b          se      pval
## 1 -0.001269811 0.004257412 0.7658199
## 2  0.001860200 0.002137132 0.3840715
## 3  0.001668861 0.001510451 0.2692132
## 4  0.004750532 0.006187746 0.4435608
## 5  0.004750532 0.004989320 0.3421867

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      MfEccK     hk2Grt outcome exposure                  MR Egger 237.5138
## 2      MfEccK     hk2Grt outcome exposure Inverse variance weighted 238.1711
##   Q_df     Q_pval
## 1  197 0.02565384
## 2  198 0.02684607
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      MfEccK     hk2Grt outcome exposure     2.55375e-05 3.45851e-05 0.4611525

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd    T-stat
## 1 beta.exposure               Raw     0.001668861 0.001510451 1.1048763
## 2 beta.exposure Outlier-corrected     0.001405855 0.001476902 0.9518946
##     P-value
## 1 0.2705540
## 2 0.3423168
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 240.5841
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.029
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs Pvalue
## 1   7.517691e-08      1
## 2   1.271457e-11      1
## 3   8.992182e-08      1
## 4   6.527456e-09      1
## 5   3.302688e-09      1
## 6   1.348771e-08      1
## 7   7.440307e-09      1
## 8   5.546649e-10      1
## 9   3.157258e-08      1
## 10  7.436410e-08      1
## 11  2.026015e-08      1
## 12  6.089736e-08      1
## 13  8.226630e-09      1
## 14  3.245455e-08      1
## 15  1.113986e-09      1
## 16  1.989723e-08      1
## 17  1.176837e-09      1
## 18  1.444003e-08      1
## 19  6.216653e-09      1
## 20  1.387624e-07      1
## 21  5.826380e-09      1
## 22  1.780977e-09      1
## 23  2.522604e-08      1
## 24  1.262028e-07      1
## 25  8.277351e-08      1
## 26  6.313185e-11      1
## 27  2.039514e-08      1
## 28  8.460995e-08      1
## 29  1.299840e-08      1
## 30  4.431577e-08      1
## 31  2.858516e-08      1
## 32  9.396671e-08      1
## 33  1.287885e-07      1
## 34  6.825920e-09      1
## 35  1.771519e-08      1
## 36  1.017379e-10      1
## 37  2.895997e-08      1
## 38  7.929748e-10      1
## 39  3.947904e-08      1
## 40  3.352432e-08      1
## 41  2.366309e-08      1
## 42  1.266446e-07      1
## 43  3.923154e-09      1
## 44  3.954464e-08      1
## 45  9.792375e-08      1
## 46  5.811787e-08      1
## 47  1.876018e-10      1
## 48  4.631179e-09      1
## 49  3.697454e-08      1
## 50  5.768256e-09      1
## 51  3.085578e-08      1
## 52  2.272024e-07      1
## 53  3.862546e-08      1
## 54  9.645274e-10      1
## 55  5.145913e-09      1
## 56  2.789418e-08      1
## 57  3.248783e-09      1
## 58  1.057350e-08      1
## 59  2.029285e-09      1
## 60  6.770080e-09      1
## 61  8.958385e-08      1
## 62  5.016072e-07      1
## 63  4.424039e-08      1
## 64  1.722991e-09      1
## 65  1.422302e-08      1
## 66  4.673635e-08      1
## 67  2.283582e-10      1
## 68  4.867976e-09      1
## 69  6.387049e-08      1
## 70  1.302530e-14      1
## 71  2.193830e-10      1
## 72  3.168007e-09      1
## 73  1.540658e-10      1
## 74  1.886432e-09      1
## 75  3.298590e-09      1
## 76  3.169772e-09      1
## 77  6.138605e-08      1
## 78  3.424400e-10      1
## 79  2.521307e-11      1
## 80  9.267750e-08      1
## 81  5.244286e-09      1
## 82  5.566801e-10      1
## 83  1.026163e-08      1
## 84  1.613211e-07      1
## 85  9.643017e-09      1
## 86  1.553503e-07      1
## 87  4.414635e-08      1
## 88  2.028242e-09      1
## 89  6.157915e-08      1
## 90  6.013710e-10      1
## 91  9.645818e-08      1
## 92  1.193181e-08      1
## 93  4.207485e-08      1
## 94  1.601974e-08      1
## 95  2.573316e-08      1
## 96  1.057498e-08      1
## 97  7.371938e-09      1
## 98  1.561171e-08      1
## 99  1.688617e-08      1
## 100 4.647174e-12      1
## 101 3.871144e-08      1
## 102 7.966858e-09      1
## 103 2.603926e-09      1
## 104 1.226622e-09      1
## 105 4.260486e-09      1
## 106 5.755723e-08      1
## 107 1.775891e-09      1
## 108 8.019706e-08      1
## 109 1.085389e-11      1
## 110 1.161823e-07      1
## 111 1.714215e-09      1
## 112 5.381390e-09      1
## 113 4.406567e-08      1
## 114 8.216829e-09      1
## 115 1.217072e-08      1
## 116 1.448906e-08      1
## 117 3.899343e-11      1
## 118 3.542305e-08      1
## 119 4.058911e-08      1
## 120 7.351878e-08      1
## 121 2.734764e-08      1
## 122 5.098990e-10      1
## 123 4.378023e-08      1
## 124 4.252995e-08      1
## 125 8.384509e-09      1
## 126 6.068484e-10      1
## 127 1.961639e-07      1
## 128 1.650664e-08      1
## 129 2.375269e-09      1
## 130 1.070594e-07      1
## 131 6.268891e-08      1
## 132 1.241526e-08      1
## 133 5.345562e-08      1
## 134 2.606111e-08      1
## 135 2.629170e-10      1
## 136 2.415578e-08      1
## 137 1.517659e-08      1
## 138 1.733583e-08      1
## 139 2.878326e-09      1
## 140 5.497251e-10      1
## 141 1.052341e-08      1
## 142 8.026045e-09      1
## 143 3.003803e-08      1
## 144 6.927187e-08      1
## 145 6.952417e-08      1
## 146 2.169303e-08      1
## 147 4.649198e-09      1
## 148 5.891687e-09      1
## 149 7.639013e-09      1
## 150 3.400453e-09      1
## 151 6.171273e-09      1
## 152 8.749325e-08      1
## 153 3.003729e-10      1
## 154 2.030090e-10      1
## 155 6.739578e-07 <0.199
## 156 5.608521e-09      1
## 157 4.727435e-09      1
## 158 3.719203e-09      1
## 159 9.673984e-08      1
## 160 6.731137e-08      1
## 161 4.432076e-08      1
## 162 1.213806e-08      1
## 163 1.176652e-08      1
## 164 5.929749e-09      1
## 165 4.164943e-10      1
## 166 1.110464e-08      1
## 167 2.333890e-10      1
## 168 2.996059e-08      1
## 169 3.602197e-07      1
## 170 1.195177e-08      1
## 171 8.589169e-08      1
## 172 1.584854e-08      1
## 173 1.712310e-10      1
## 174 5.338408e-08      1
## 175 9.580536e-09      1
## 176 4.129467e-08      1
## 177 1.148222e-08      1
## 178 3.271415e-08      1
## 179 1.141810e-08      1
## 180 1.209353e-07      1
## 181 3.762199e-08      1
## 182 3.344149e-08      1
## 183 2.122518e-09      1
## 184 1.860690e-10      1
## 185 3.673720e-09      1
## 186 9.075614e-08      1
## 187 3.876631e-08      1
## 188 1.040749e-11      1
## 189 1.568734e-08      1
## 190 8.114803e-09      1
## 191 6.725634e-09      1
## 192 8.631564e-08      1
## 193 4.797815e-09      1
## 194 3.824765e-08      1
## 195 2.468899e-11      1
## 196 1.589328e-08      1
## 197 7.021538e-11      1
## 198 9.353807e-08      1
## 199 1.628477e-08      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 155
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##       18.7079 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.816

Radial test

## 
## Radial IVW
## 
##                     Estimate   Std.Error  t value  Pr(>|t|)
## Effect (Mod.2nd) 0.001668861 0.001510451 1.104876 0.2692133
## Iterative        0.001668861 0.001510451 1.104876 0.2692133
## Exact (FE)       0.001691148 0.001377279 1.227890 0.2194881
## Exact (RE)       0.001697580 0.001547802 1.096768 0.2740749
## 
## 
## Residual standard error: 1.097 on 198 degrees of freedom
## 
## F-statistic: 1.22 on 1 and 198 DF, p-value: 0.271
## Q-Statistic for heterogeneity: 238.1419 on 198 DF , p-value: 0.02692668
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##         24         52         62         86         91        127        155 
## 0.07184201 0.03890703 0.12925860 0.15149717 0.04250918 0.11267649 0.08524017 
##        159        169 
## 0.03709560 0.16263814
## [1]  20  52  62  84  86 127 155 169

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      MfEccK     hk2Grt outcome exposure                  MR Egger  167
## 2      MfEccK     hk2Grt outcome exposure           Weighted median  167
## 3      MfEccK     hk2Grt outcome exposure Inverse variance weighted  167
## 4      MfEccK     hk2Grt outcome exposure               Simple mode  167
## 5      MfEccK     hk2Grt outcome exposure             Weighted mode  167
##               b          se      pval
## 1  0.0010196479 0.004707716 0.8287948
## 2  0.0008035741 0.002325282 0.7296573
## 3 -0.0004145744 0.001576751 0.7926049
## 4  0.0051598515 0.006219085 0.4079112
## 5  0.0038014567 0.004411757 0.3901149

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      MfEccK     hk2Grt outcome exposure                  MR Egger 106.5795
## 2      MfEccK     hk2Grt outcome exposure Inverse variance weighted 106.6840
##   Q_df    Q_pval
## 1  165 0.9998751
## 2  166 0.9998979
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      MfEccK     hk2Grt outcome exposure   -1.186155e-05 3.668582e-05
##        pval
## 1 0.7468564

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      MfEccK     hk2Grt outcome exposure                  MR Egger  167
## 2      MfEccK     hk2Grt outcome exposure           Weighted median  167
## 3      MfEccK     hk2Grt outcome exposure Inverse variance weighted  167
## 4      MfEccK     hk2Grt outcome exposure               Simple mode  167
## 5      MfEccK     hk2Grt outcome exposure             Weighted mode  167
##               b          se      pval        lo_ci       up_ci        or
## 1  0.0010196479 0.004707716 0.8287948 -0.008207475 0.010246771 1.0010202
## 2  0.0008035741 0.002325282 0.7296573 -0.003753978 0.005361126 1.0008039
## 3 -0.0004145744 0.001576751 0.7926049 -0.003505006 0.002675857 0.9995855
## 4  0.0051598515 0.006219085 0.4079112 -0.007029555 0.017349258 1.0051732
## 5  0.0038014567 0.004411757 0.3901149 -0.004845587 0.012448501 1.0038087
##    or_lci95 or_uci95
## 1 0.9918261 1.010299
## 2 0.9962531 1.005376
## 3 0.9965011 1.002679
## 4 0.9929951 1.017501
## 5 0.9951661 1.012526

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 167 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.000     0.002 -0.004, 0.003   0.793
## ------------------------------------------------------------------
## Residual standard error =  0.802 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 106.6840 on 166 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%. 
## F statistic = 54.7.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.001     0.002  -0.004 0.005   0.763
##            Weighted median    0.001     0.002  -0.004 0.005   0.729
##  Penalized weighted median    0.001     0.002  -0.004 0.005   0.712
##                                                                    
##                        IVW    0.000     0.002  -0.004 0.003   0.793
##              Penalized IVW    0.000     0.002  -0.004 0.003   0.793
##                 Robust IVW    0.000     0.001  -0.003 0.002   0.807
##       Penalized robust IVW    0.000     0.001  -0.003 0.002   0.807
##                                                                    
##                   MR-Egger    0.001     0.005  -0.008 0.010   0.829
##                (intercept)    0.000     0.000   0.000 0.000   0.746
##         Penalized MR-Egger    0.001     0.005  -0.008 0.010   0.829
##                (intercept)    0.000     0.000   0.000 0.000   0.746
##            Robust MR-Egger    0.001     0.004  -0.006 0.008   0.760
##                (intercept)    0.000     0.000   0.000 0.000   0.697
##  Penalized robust MR-Egger    0.001     0.004  -0.006 0.008   0.760
##                (intercept)    0.000     0.000   0.000 0.000   0.697

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
MfEccK hk2Grt exposure outcome 0.0197378 0.0002854 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] -0.0004194714
## 
## $beta.se
## [1] 0.001611633
## 
## $beta.p.value
## [1] 0.7946499
## 
## $naive.se
## [1] 0.001596741
## 
## $chi.sq.test
## [1] 106.6832
##   over.dispersion loss.function      beta.hat     beta.se
## 1           FALSE            l2 -0.0004194714 0.001611633
## 2           FALSE         huber -0.0004355307 0.001653500
## 3           FALSE         tukey -0.0003694527 0.001653499
## 4            TRUE            l2 -0.0004078740 0.001861652
## 5            TRUE         huber -0.0004353488 0.001653500
## 6            TRUE         tukey -0.0003696686 0.001653500
## 
## MR-Lasso method 
## 
## Number of variants : 167 
## Number of valid instruments : 167 
## Tuning parameter : 0.1614645 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure    0.000     0.002 -0.004, 0.003   0.793
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  167 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC    0.000 0.002  0.793 [-0.004,0.003]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 167 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.000     0.002 -0.004, 0.003   0.793   694.209
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 167 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.004     0.004 -0.005, 0.012   0.388
## ------------------------------------------------------------------

SBP on BC

Introduction

  • Title: Investigating the causality between SBP on BC

Data Preparation

1- Number of total SNPs in exposure: 7,088,083 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 74,125 SNPs

3- Number of SNPs exposure after clumping : 456 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 456 SNPs

6- Number of SNPs after harmonization (action=2) = 441 SNPs

(rs1012089, rs11585169, rs11967262, rs12321, rs17610485, rs1870735, rs2024385, rs3802517, rs3828282, rs3845811, rs4834792, rs7310615, rs7463212, rs7796, rs961764 being palindromic and were removed)

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.72   38.08   50.39   75.07   76.22  627.55

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      ufy4y1     hk2Grt outcome exposure                  MR Egger  441
## 2      ufy4y1     hk2Grt outcome exposure           Weighted median  441
## 3      ufy4y1     hk2Grt outcome exposure Inverse variance weighted  441
## 4      ufy4y1     hk2Grt outcome exposure               Simple mode  441
## 5      ufy4y1     hk2Grt outcome exposure             Weighted mode  441
##               b           se      pval
## 1 -2.253819e-05 6.467707e-05 0.7276523
## 2 -1.893980e-06 3.871551e-05 0.9609827
## 3  1.743286e-05 2.567725e-05 0.4971871
## 4 -6.396224e-05 1.222661e-04 0.6011403
## 5 -3.554654e-05 8.961968e-05 0.6918270

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      ufy4y1     hk2Grt outcome exposure                  MR Egger 482.7800
## 2      ufy4y1     hk2Grt outcome exposure Inverse variance weighted 483.2787
##   Q_df     Q_pval
## 1  439 0.07305894
## 2  440 0.07550695
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      ufy4y1     hk2Grt outcome exposure    1.336164e-05 1.984127e-05
##        pval
## 1 0.5010303

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd    T-stat
## 1 beta.exposure               Raw    1.743286e-05 2.567725e-05 0.6789223
## 2 beta.exposure Outlier-corrected              NA           NA        NA
##     P-value
## 1 0.4975441
## 2        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 485.438
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.078

Radial test

## 
## Radial IVW
## 
##                      Estimate    Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 1.743287e-05 2.567725e-05 0.6789228 0.4971868
## Iterative        1.743286e-05 2.567725e-05 0.6789223 0.4971871
## Exact (FE)       1.544891e-05 2.450071e-05 0.6305498 0.5283350
## Exact (RE)       3.259713e-05 3.499166e-05 0.9315685 0.3520704
## 
## 
## Residual standard error: 1.048 on 440 degrees of freedom
## 
## F-statistic: 0.46 on 1 and 440 DF, p-value: 0.498
## Q-Statistic for heterogeneity: 483.2714 on 440 DF , p-value: 0.07554011
## 
##  No significant outliers 
## Number of iterations = 1
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##         12         22         29         35         57         76         83 
## 0.01759063 0.01069175 0.11242044 0.02534383 0.05728427 0.01457870 0.01426455 
##        110        148        170        206        218        219        229 
## 0.04941212 0.17537897 0.01758714 0.01072930 0.01509872 0.01899798 0.03924269 
##        284        287        326        347        379        400        406 
## 0.03989497 0.02942982 0.21102661 0.07100033 0.03452196 0.01242249 0.02355500
##  [1]   6  12  29  34  57  65  75 102 110 122 125 148 170 206 218 264 284 287 326
## [20] 347 354 379 385 400 406

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      ufy4y1     hk2Grt outcome exposure                  MR Egger  408
## 2      ufy4y1     hk2Grt outcome exposure           Weighted median  408
## 3      ufy4y1     hk2Grt outcome exposure Inverse variance weighted  408
## 4      ufy4y1     hk2Grt outcome exposure               Simple mode  408
## 5      ufy4y1     hk2Grt outcome exposure             Weighted mode  408
##               b           se       pval
## 1  5.370326e-05 7.001831e-05 0.44353395
## 2  2.090026e-05 4.025492e-05 0.60362287
## 3  4.601377e-05 2.659357e-05 0.08358391
## 4 -4.264975e-05 1.148409e-04 0.71054699
## 5 -6.373503e-08 8.402062e-05 0.99939513

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      ufy4y1     hk2Grt outcome exposure                  MR Egger 348.8775
## 2      ufy4y1     hk2Grt outcome exposure Inverse variance weighted 348.8916
##   Q_df    Q_pval
## 1  406 0.9813971
## 2  407 0.9829522
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      ufy4y1     hk2Grt outcome exposure   -2.443788e-06 2.058497e-05
##        pval
## 1 0.9055582

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      ufy4y1     hk2Grt outcome exposure                  MR Egger  408
## 2      ufy4y1     hk2Grt outcome exposure           Weighted median  408
## 3      ufy4y1     hk2Grt outcome exposure Inverse variance weighted  408
## 4      ufy4y1     hk2Grt outcome exposure               Simple mode  408
## 5      ufy4y1     hk2Grt outcome exposure             Weighted mode  408
##               b           se       pval         lo_ci        up_ci        or
## 1  5.370326e-05 7.001831e-05 0.44353395 -8.353263e-05 1.909391e-04 1.0000537
## 2  2.090026e-05 4.025492e-05 0.60362287 -5.799938e-05 9.979990e-05 1.0000209
## 3  4.601377e-05 2.659357e-05 0.08358391 -6.109617e-06 9.813716e-05 1.0000460
## 4 -4.264975e-05 1.148409e-04 0.71054699 -2.677380e-04 1.824385e-04 0.9999574
## 5 -6.373503e-08 8.402062e-05 0.99939513 -1.647442e-04 1.646167e-04 0.9999999
##    or_lci95 or_uci95
## 1 0.9999165 1.000191
## 2 0.9999420 1.000100
## 3 0.9999939 1.000098
## 4 0.9997323 1.000182
## 5 0.9998353 1.000165

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 408 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.000     0.000 0.000, 0.000   0.084
## ------------------------------------------------------------------
## Residual standard error =  0.926 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 348.8916 on 407 degrees of freedom, (p-value = 0.9830). I^2 = 0.0%. 
## F statistic = 68.8.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.000     0.000   0.000 0.000   0.555
##            Weighted median    0.000     0.000   0.000 0.000   0.576
##  Penalized weighted median    0.000     0.000   0.000 0.000   0.579
##                                                                    
##                        IVW    0.000     0.000   0.000 0.000   0.084
##              Penalized IVW    0.000     0.000   0.000 0.000   0.084
##                 Robust IVW    0.000     0.000   0.000 0.000   0.059
##       Penalized robust IVW    0.000     0.000   0.000 0.000   0.059
##                                                                    
##                   MR-Egger    0.000     0.000   0.000 0.000   0.443
##                (intercept)    0.000     0.000   0.000 0.000   0.905
##         Penalized MR-Egger    0.000     0.000   0.000 0.000   0.443
##                (intercept)    0.000     0.000   0.000 0.000   0.905
##            Robust MR-Egger    0.000     0.000   0.000 0.000   0.264
##                (intercept)    0.000     0.000   0.000 0.000   0.802
##  Penalized robust MR-Egger    0.000     0.000   0.000 0.000   0.264
##                (intercept)    0.000     0.000   0.000 0.000   0.802

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
ufy4y1 hk2Grt exposure outcome 0.0370454 0.0009415 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] 4.658926e-05
## 
## $beta.se
## [1] 2.701764e-05
## 
## $beta.p.value
## [1] 0.08463538
## 
## $naive.se
## [1] 2.682018e-05
## 
## $chi.sq.test
## [1] 348.8541
##   over.dispersion loss.function     beta.hat      beta.se
## 1           FALSE            l2 4.658926e-05 2.701764e-05
## 2           FALSE         huber 4.529768e-05 2.771934e-05
## 3           FALSE         tukey 4.468224e-05 2.771931e-05
## 4            TRUE            l2 4.786712e-05 2.996283e-05
## 5            TRUE         huber 4.786712e-05 2.771972e-05
## 6            TRUE         tukey 4.786712e-05 2.771977e-05
## 
## MR-Lasso method 
## 
## Number of variants : 408 
## Number of valid instruments : 408 
## Tuning parameter : 0.1151046 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.000     0.000 0.000, 0.000   0.084
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  408 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.000 0.000  0.081 [0.000,0.000]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 408 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.000     0.000 0.000, 0.000   0.084  1369.568
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 408 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.000     0.000 0.000, 0.000   0.999
## ------------------------------------------------------------------

FBG on BC

Introduction

  • Title: Investigating the causality between FBS on BC

Data Preparation

1- Number of total SNPs in exposure: 105,585 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 107 SNPs

3- Number of SNPs exposure after clumping : 80 SNPs

4- Number of total SNPs in outcome: 9,904,926 SNPs

5- Number of common variants between exposure and outcome: 27 SNPs

6- Number of SNPs after harmonization (action=2) = 27 SNPs

Checking weakness of the instruments:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   15.45   21.17   27.50   67.77   40.96  519.36

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      HC7LDU     hk2Grt outcome exposure                  MR Egger   23
## 2      HC7LDU     hk2Grt outcome exposure           Weighted median   23
## 3      HC7LDU     hk2Grt outcome exposure Inverse variance weighted   23
## 4      HC7LDU     hk2Grt outcome exposure               Simple mode   23
## 5      HC7LDU     hk2Grt outcome exposure             Weighted mode   23
##               b           se      pval
## 1 -1.035502e-04 0.0018656098 0.9562610
## 2 -1.034450e-03 0.0014175453 0.4655447
## 3  1.634319e-04 0.0009975402 0.8698611
## 4 -1.826525e-03 0.0024242238 0.4591693
## 5  3.313507e-05 0.0012753330 0.9795063

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      HC7LDU     hk2Grt outcome exposure                  MR Egger 22.97279
## 2      HC7LDU     hk2Grt outcome exposure Inverse variance weighted 23.00476
##   Q_df    Q_pval
## 1   21 0.3454308
## 2   22 0.4014611
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      HC7LDU     hk2Grt outcome exposure    1.078169e-05 6.30744e-05 0.8659103

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw    0.0001634319 0.0009975402 0.163835
## 2 beta.exposure Outlier-corrected              NA           NA       NA
##     P-value
## 1 0.8713569
## 2        NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 25.02173
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.447

Radial test

## 
## Radial IVW
## 
##                      Estimate    Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 0.0001634276 0.0009975406 0.1638306 0.8698645
## Iterative        0.0001634276 0.0009975406 0.1638306 0.8698645
## Exact (FE)       0.0001657918 0.0009755219 0.1699519 0.8650480
## Exact (RE)       0.0001654286 0.0009346680 0.1769918 0.8611342
## 
## 
## Residual standard error: 1.023 on 22 degrees of freedom
## 
## F-statistic: 0.03 on 1 and 22 DF, p-value: 0.871
## Q-Statistic for heterogeneity: 23.00436 on 22 DF , p-value: 0.4014837
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

Studentized residuals:

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).

Potential Outliers and Influential SNPs

##        11        15 
## 0.8849746 0.2038728
## [1] 11

report After Deleting Influential SNPs:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      HC7LDU     hk2Grt outcome exposure                  MR Egger   22
## 2      HC7LDU     hk2Grt outcome exposure           Weighted median   22
## 3      HC7LDU     hk2Grt outcome exposure Inverse variance weighted   22
## 4      HC7LDU     hk2Grt outcome exposure               Simple mode   22
## 5      HC7LDU     hk2Grt outcome exposure             Weighted mode   22
##               b           se      pval
## 1 -1.275713e-04 0.0018264414 0.9450092
## 2 -1.042590e-03 0.0013420010 0.4372223
## 3 -1.458760e-05 0.0009834775 0.9881657
## 4 -1.731827e-03 0.0022996324 0.4597566
## 5  1.248827e-05 0.0013174349 0.9925263

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      HC7LDU     hk2Grt outcome exposure                  MR Egger 20.96791
## 2      HC7LDU     hk2Grt outcome exposure Inverse variance weighted 20.97367
##   Q_df    Q_pval
## 1   20 0.3990238
## 2   21 0.4605532
##   id.exposure id.outcome outcome exposure egger_intercept           se
## 1      HC7LDU     hk2Grt outcome exposure    4.590454e-06 6.190946e-05
##        pval
## 1 0.9416293

OR report:

##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      HC7LDU     hk2Grt outcome exposure                  MR Egger   22
## 2      HC7LDU     hk2Grt outcome exposure           Weighted median   22
## 3      HC7LDU     hk2Grt outcome exposure Inverse variance weighted   22
## 4      HC7LDU     hk2Grt outcome exposure               Simple mode   22
## 5      HC7LDU     hk2Grt outcome exposure             Weighted mode   22
##               b           se      pval        lo_ci       up_ci        or
## 1 -1.275713e-04 0.0018264414 0.9450092 -0.003707397 0.003452254 0.9998724
## 2 -1.042590e-03 0.0013420010 0.4372223 -0.003672912 0.001587732 0.9989580
## 3 -1.458760e-05 0.0009834775 0.9881657 -0.001942203 0.001913028 0.9999854
## 4 -1.731827e-03 0.0022996324 0.4597566 -0.006239107 0.002775452 0.9982697
## 5  1.248827e-05 0.0013174349 0.9925263 -0.002569684 0.002594661 1.0000125
##    or_lci95 or_uci95
## 1 0.9962995 1.003458
## 2 0.9963338 1.001589
## 3 0.9980597 1.001915
## 4 0.9937803 1.002779
## 5 0.9974336 1.002598

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 22 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.000     0.001 -0.002, 0.002   0.988
## ------------------------------------------------------------------
## Residual standard error =  0.999 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 20.9737 on 21 degrees of freedom, (p-value = 0.4606). I^2 = 0.0%. 
## F statistic = 69.7.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median   -0.001     0.002  -0.004 0.002   0.510
##            Weighted median   -0.001     0.001  -0.004 0.002   0.442
##  Penalized weighted median   -0.001     0.001  -0.004 0.002   0.442
##                                                                    
##                        IVW    0.000     0.001  -0.002 0.002   0.988
##              Penalized IVW    0.000     0.001  -0.002 0.002   0.988
##                 Robust IVW    0.000     0.001  -0.002 0.002   0.974
##       Penalized robust IVW    0.000     0.001  -0.002 0.002   0.974
##                                                                    
##                   MR-Egger    0.000     0.002  -0.004 0.003   0.944
##                (intercept)    0.000     0.000   0.000 0.000   0.941
##         Penalized MR-Egger    0.000     0.002  -0.004 0.003   0.944
##                (intercept)    0.000     0.000   0.000 0.000   0.941
##            Robust MR-Egger    0.000     0.002  -0.003 0.003   0.983
##                (intercept)    0.000     0.000   0.000 0.000   0.996
##  Penalized robust MR-Egger    0.000     0.002  -0.003 0.003   0.983
##                (intercept)    0.000     0.000   0.000 0.000   0.996

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
HC7LDU hk2Grt exposure outcome 0.0468254 5.61e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

MRraps package

## $beta.hat
## [1] -1.478242e-05
## 
## $beta.se
## [1] 0.000998601
## 
## $beta.p.value
## [1] 0.9881892
## 
## $naive.se
## [1] 0.0009913349
## 
## $chi.sq.test
## [1] 20.97367
##   over.dispersion loss.function      beta.hat     beta.se
## 1           FALSE            l2 -1.478242e-05 0.000998601
## 2           FALSE         huber -2.661156e-06 0.001024542
## 3           FALSE         tukey -3.333910e-05 0.001024545
## 4            TRUE            l2 -9.726443e-05 0.001131137
## 5            TRUE         huber -6.804823e-06 0.001024542
## 6            TRUE         tukey -3.402461e-05 0.001024545
## 
## MR-Lasso method 
## 
## Number of variants : 22 
## Number of valid instruments : 22 
## Tuning parameter : 0.5001954 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure    0.000     0.001 -0.002, 0.002   0.988
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  22 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC    0.000 0.001  0.999 [-0.002,0.002]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 22 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.000     0.001 -0.002, 0.002   0.988   322.452
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 22 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.000     0.001 -0.002, 0.002   0.991
## ------------------------------------------------------------------